Question: The output voltage of a power supply is assumed to be normally distributed. Sixteen observations taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38, 10.85.

1. Test the hypothesis that the mean voltage equals 12 V against a two-sided alternative using \(\alpha \) = 0.05.
2. Construct a 95% two-sided confidence interval on \(\mu \).
3. Test the hypothesis that \({{\sigma }^{2}}\) = 11 using \(\alpha \) = 0.05.
4. Construct a 95% two-sided confidence interval on \(\sigma \).
5. Construct a 95% upper confidence interval on \(\mu \).
6. Does the assumption of normality seem reasonable for the output voltage?

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